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1. In a 90 litres mixture of water and milk, the water is 30%. How many litres of water is required to increase the percentage of water in the mixture to 40%?

2. Priya was married to Rajesh at the age of 24 years. Her present age is 4/3 times her age at the time of marriage. The present age of their son is 18.75% of the age of Priya at present. Rajesh is 29 years older to his son, then find the age of Rajesh at the time of his marriage.

3. The base radii of two cylinders are in the ratio of 3:4 and their heights are in the ratio of 7:6. The ratio of their volume is

4. A shopkeeper sold 24 shirts at a profit of 20% and 16 shirts at a profit of 10%. If he had sold all the 40 shirts at a profit of 15%, then his profit would have been reduced by Rs. 36. What is the cost price of each shirt?

5. Raju bought a bike whose sale price was Rs. 50,000. He availed 30% discount on it under exchange offer and then 20% discount as credit card discount. Then he spent 15% of its sale price on its maintenance. At what price should he sell that bike to earn 15% profit?

6. A coaching center has increased the tuition fee by 30 % and simultaneously the number of students is decreased by 10%. What is the percentage change in the total amount collected by coaching centre?

7. P, Q and R started a business by investing ½, 1/3rd and 1/6th of the capital respectively. After 1/3rd of the total time, P withdrew his capital completely and after 1/4th of the total time Q withdrew his capital. R kept his capital for the full period. The ratio in which the total profit is to be divided amongst the partners is

8. At what interest rate will a sum of money double itself in 3 years if the interest is compounded annually?

9. A bus covered a certain distance from village A to village B at the speed of 60 km/hr. However on its return journey it got stuck in traffic and covered the same distance at the speed of 40 km/hr and took 2 hours more to reach Its destination. What is the distance between village A and B?

10. A cistern has 3 pipes A, B and C. A and B can fill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 p.m. respectively, at what time will the cistern be empty?

**Check your Answers below: **

##### 1. Question

In a 90 litres mixture of water and milk, the water is 30%. How many litres of water is required to increase the percentage of water in the mixture to 40%?

Ans:3

Milk :Water = 7:3

i.e quantity of water = 3/10 × 90 =27litres

and quantity of milk = 63

Now required ratio is 6:4 i.e. 3:2

Quantity of milk =63 =3x/5

=>x= 105 litres

i.e. required quantity of water = 42litres

Increase = 42 – 27 =15 litres. Hence, option c.##### 2. Question

Priya was married to Rajesh at the age of 24 years. Her present age is 4/3 times her age at the time of marriage. The present age of their son is 18.75% of the age of Priya at present. Rajesh is 29 years older to his son, then find the age of Rajesh at the time of his marriage.

Ans:4

Age of priya at present = 24 * (4/3) = 32 years

Present age of their son = 18.75% of 32 = 6 years

Present age of Rajesh = 6 + 29 = 35 years

Since Rajesh got married before 8 years from present. So, age of Rajesh at the time of his marriage = 35 – 8 = 27 years##### 3. Question

The base radii of two cylinders are in the ratio of 3:4 and their heights are in the ratio of 7:6. The ratio of their volume is

Ans:1

R1:R2=3:4H1:H2=7:6Volume1/volume2=π(R1)

^{2}H/π(R2)^{2}H=3^{2}*7/4^{2}*6=21:32##### 4. Question

A shopkeeper sold 24 shirts at a profit of 20% and 16 shirts at a profit of 10%. If he had sold all the 40 shirts at a profit of 15%, then his profit would have been reduced by Rs. 36. What is the cost price of each shirt?

Ans:3

Let the cost price of each shirt be Rs. x, therefore, 24 × 1.2x + 16 × 1.1x – 40 × 1.15x = Rs. 36, solving we get x = Rs. 90. Hence, option c.##### 5. Question

Raju bought a bike whose sale price was Rs. 50,000. He availed 30% discount on it under exchange offer and then 20% discount as credit card discount. Then he spent 15% of its sale price on its maintenance. At what price should he sell that bike to earn 15% profit?

Ans:1

Price = Rs. 50,000.

After 30% discount, Price= Rs. 35000

After, 20% discount on this, Price = Rs. 28000

CP for Raju = Rs. 28000 +(15% of 50,000) = Rs. 35,500

SP = 1.15 * 35500 = Rs. 40825. Hence, option a.##### 6. Question

A coaching center has increased the tuition fee by 30 % and simultaneously the number of students is decreased by 10%. What is the percentage change in the total amount collected by coaching centre?

Ans:2

Let the tuition fee be y and number of students be x.

Total amount collected = xy

Now,

Tuition fee = x + 0.3x = 1.3x

Number of students = y – 0.1y = 0.9y

Total amount = 1.3x * 0.9y = 1.17xy

Change =1.17xy – xy = 0.17xy

i.e, 17% increase. Hence, option b.##### 7. Question

P, Q and R started a business by investing ½, 1/3rd and 1/6th of the capital respectively. After 1/3rd of the total time, P withdrew his capital completely and after 1/4th of the total time Q withdrew his capital. R kept his capital for the full period. The ratio in which the total profit is to be divided amongst the partners is

Ans:3

Let X be the total investment for total time period Y

P’s share = (X/2) * (Y/3)

Q’s share = (X/3) * (Y/4)

R’s share = (X/6) * Y

Required ratio = 1/6 : 1/12 : 1/6 = 2:1:2##### 8. Question

At what interest rate will a sum of money double itself in 3 years if the interest is compounded annually?

Ans:2

A = P (1+ r/100)^{T}As per the question, A = 2P=> 2P = P (1 + r/100)

^{3}⇒(1 + r/100)

^{3}= 2⇒1 + r/100 = 2

^{1/3}⇒ r/100 = 2

^{1/3}– 1 = 1.26 – 1 = 0.26⇒ r = 26%

##### 9. Question

A bus covered a certain distance from village A to village B at the speed of 60 km/hr. However on its return journey it got stuck in traffic and covered the same distance at the speed of 40 km/hr and took 2 hours more to reach Its destination. What is the distance between village A and B?

Ans:1

Let the distance between A and B be ‘x’ km

Let the time taken by bus while travelling from A to B be ‘t’ hours. Therefore, time taken by the bus from B to A is ‘t+2’ hours

Time taken from A to B = t = x/60

Time taken from B to A = t + 2 = x/40

(x/60) + 2 = x/40

or x/120 = 2 or x = 240 km##### 10. Question

A cistern has 3 pipes A, B and C. A and B can fill it in 3 hours and 4 hours respectively while C can empty the completely filled cistern in 1 hour. If the pipes are opened in order at 3, 4 and 5 p.m. respectively, at what time will the cistern be empty?

Ans:2

Pipe A can fill 1/3 rd of the cistern in 1 hour

Pipe B can fill ¼ th of the cistern in 1 hour

Pipe C can empty the cistern in 1 hour

Pipe A is opened at 3 pm. By 4 pm, 1/3 rd of the tank is filled

At 4 pm, pipe B is also opened. Hence, the fraction of cistern filled between 4 pm and 5 pm = 1/3 + 1/4 = 7/12

By 5 pm, portion of the cistern filled = 1/3 + 7/12 = 11/12

At 5 pm, pipe C is opened. From 5 pm, all 3 pipes will be open

Portion of the cistern emptied in one hour when all 3 pipes are opened = 1 – 1/3 – 1/4 = (12 – 4 – 3)/12 = 5/12

Hence, to empty 11/12 th of the cistern, time taken = (11/12)/(5/12) = 2.2 hours

Time taken to empty cistern = 2.2 hours i.e. 2 hours and 12 minutes

Hence, at 7.12 pm, the cistern will be empty